Let f be the function defined as follows.

y=f (x) = (8x^2) - 2x+3

(a) Find the differential of f.

dy = (16x-2) dx

(b) Use your result from part (a) to find the approximate change in y if x changes from 2 to 1.97. (Round your answer to two decimal places.)

dy =

(c) Find the actual change in y if x changes from 2 to 1.97 and compare your result with that obtained in part (b). (Round your answer to two decimal places.)

Δy =

Question

Isabell Weber

Mathematics

2 November, 23:28

Let f be the function defined as follows.

y=f (x) = (8x^2) - 2x+3

(a) Find the differential of f.

dy = (16x-2) dx

(b) Use your result from part (a) to find the approximate change in y if x changes from 2 to 1.97. (Round your answer to two decimal places.)

dy =

(c) Find the actual change in y if x changes from 2 to 1.97 and compare your result with that obtained in part (b). (Round your answer to two decimal places.)

Δy =

+2

Answers (1)

Know the Answer?

Johnny Mcpherson · Answer 1

Y = f (x) = 8x^2 - 2x + 3

a.) dy/dx = 16x - 2

b.) dy = (16x - 2) dx

dy = (16 (2) - 2) (2 - 1.97) = 0.03 (32 - 2) = 0.03 * 30 = 0.9

dy = 0.9

c.) (8 (2) ^2 - 2 (2) + 3) - (8 (1.97) ^2 - 2 (1.97) + 3) = 31 - 30.1072 = 0.8928

Δy = 0.8928